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Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....

Impossible Einstein-Weyl geometries

Eastwood, Michael (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.

Index and dynamics of quantized contact transformations

Steven Zelditch (1997)

Annales de l'institut Fourier

Quantized contact transformations are Toeplitz operators over a contact manifold ( X , α ) of the form U χ = Π A χ Π , where Π : H 2 ( X ) → L 2 ( X ) is a Szegö projector, where χ is a contact transformation and where A is a pseudodifferential operator over X . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine ind ( U χ ) when the principal symbol is unitary, or equivalently to determine...

Inégalités de résolvante pour l’opérateur de Schrödinger avec potentiel multipolaire critique

Thomas Duyckaerts (2006)

Bulletin de la Société Mathématique de France

On étudie un opérateur de la forme - Δ + V sur ℝ d , où V est un potentiel admettant plusieurs pôles en a / r 2 . Plus précisément, on démontre l’estimation de résolvante tronquée à hautes fréquences, classique dans les cas non-captifs, et qui implique l’effet régularisant standard pour l’équation de Schrödinger correspondante. La preuve est basée sur l’introduction d’une mesure de défaut micro-locale semi-classique. On démontre également, dans le même contexte, des inégalités de Strichartz pour l’équation de Schrödinger....

Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Alice Barbara Tumpach (2009)

Annales de l’institut Fourier

In this paper, we construct a hyperkähler structure on the complexification 𝒪 ℂ of any Hermitian symmetric affine coadjoint orbit 𝒪 of a semi-simple L * -group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of 𝒪 . By a relevant identification of the complex orbit 𝒪 ℂ with the cotangent space T 𝒪 of 𝒪 induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on T 𝒪 compatible with...

Currently displaying 781 – 800 of 2284